Respuesta :
To find the area, the heptagon can be considered as consisting of seven
triangles, each having a side of the heptagon as its base.
- The area of the heptagon is approximately 2,125 cm².
Reasons:
The radius of the heptagon, r = 27.87 cm
Length of each side, s = 24.18 cm
Required:
The approximate area of the heptagon
Solution:
The area of the heptagon can be considered as consisting of seven triangles
From Pythagorean theorem, we have;
[tex]\displaystyle Height \ of \ each \ triangle, \ h = \mathbf{\sqrt{r^2 + \left(\frac{s}{2} \right)^2 }}[/tex]
[tex]\displaystyle Area \ of \ each \ triangle, \ A = \mathbf{ \frac{s}{2} \times h}[/tex]
Which gives;
[tex]\displaystyle Area \ of \ heptagon, \ A_{heptagon} =7 \times \frac{s}{2} \times h = \mathbf{7 \times \frac{s}{2} \times \sqrt{r^2 + \left(\frac{s}{2} \right)^2 }}[/tex]
Plugging in the values gives;
[tex]\displaystyle Area \ of \ heptagon, \ A_{heptagon} = 7 \times \frac{24.18}{2} \times \sqrt{27.87^2 - \left(\frac{24.18}{2} \right)^2 } \approx \mathbf{2,125.15}[/tex]
The area of the heptagon given to the nearest whole number is therefore;
- [tex]A_{heptagon}[/tex] ≈ 2,125 cm²
Learn more about finding the area of a regular polygon here:
https://brainly.com/question/4227992
